This question is from NCERT Book class 10th Ch. no.5 Ex. 5.2 Q. 1 . In this question you have to find the right option and support your answer by giving its solution. Answer the question with brief explanation.

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# Choose the correct choice in the following and justify. (i) 30th term of the A.P: 10,7, 4, …, is (A) 97 (B) 77 (C) −77 (D) −87

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(i) Given here,

A.P. = 10, 7, 4, …

Therefore, we can find,

First term, a = 10

Common difference, d = a2 − a1 = 7−10 = −3

As we know, for an A.P.,

an = a +(n−1)d

Putting the values;

a30 = 10+(30−1)(−3)

a30 = 10+(29)(−3)

a30 = 10−87 = −77

Hence, the correct answer is option C.

(ii) Given here,

A.P. = -3, -1/2, ,2 …

Therefore, we can find,

First term a = – 3

Common difference, d = a2 − a1 = (-1/2) -(-3)

⇒(-1/2) + 3 = 5/2

As we know, for an A.P.,

an = a+(n−1)d

Putting the values;

a11 = 3+(11-1)(5/2)

a11 = 3+(10)(5/2)

a11 = -3+25

a11 = 22

Hence, the answer is option B.